


the calculus of affection

by snowandfire



Category: Avatar: The Last Airbender
Genre: Alternate Universe - High School, Alternate Universe - Modern Setting, Calculus, Eventual Romance, Gay Zuko (Avatar), Iroh (Avatar) is a Good Uncle, Light Angst, M/M, Ozai (Avatar) Being a Terrible Parent, Slow Burn, Smart Sokka (Avatar), Tutoring, but they're both good at love, sokka is a calc tutor, zuko is bad at math
Language: English
Status: In-Progress
Published: 2020-07-14
Updated: 2020-12-10
Packaged: 2021-03-04 20:35:21
Rating: Teen And Up Audiences
Warnings: No Archive Warnings Apply
Chapters: 4
Words: 12,706
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/25252471
Author URL: https://archiveofourown.org/users/snowandfire/pseuds/snowandfire
Summary: [“If you’re a genius. How can you act so stupid?!” Zuko asks, aghast.Sokka moonwalks away from him, “Like this.”Or: sokka tutors zuko in calculus, a story in three parts]
Relationships: Sokka/Zuko (Avatar)
Comments: 118
Kudos: 684





	1. Differential I

> _Differential calculus divides things into small (different) pieces and tells us how they change from one moment to the next_

Sokka is three years old when he starts counting everything. One hundred ninety-nine steps to the family store, The Stop & Shop. Eleven bus stops between their house and school. Five people in his family: Katara, himself, mom, dad, and gran-gran. Dad works seven days a week. 

At three, Zuko barely perceives numbers. He likes colors. Finger painting with bright reds and greens. Picking dandelions. He’s over the moon when his mother gets him a red _Elmo_ doll that talks when you squeeze his stomach. He’s too young to notice how tired she looks. 

Sokka is five years old when the teachers call in his parents to tell them he’s ‘gifted’ and could do well with the right instruction. His parents pool all their money and savings to put him and Katara into a new, private school. The new school is an hour’s ride from the run-down part of town where they live. The kids there don’t look like him and his sister. It’s hard to make friends. But he tries to be brave, dad said this is so they can have their ‘best chance’. Dad works so hard. He has to make it work. 

When Zuko is five it’s the first time he realises his little sister is smarter than him. She can do sums and multiplication. She knows all the times tables up to thirty-five by heart. She can even read. Not baby books, but full, thick chapter books. His father is so proud. It’s the first time he stays up all night trying to figure out math. But it’s no use. The numbers make his head swim.

He hears her chant in his mind when he goes to sleep, “Zuzu is a dum-dum! Zuzu is a dum-dum!” 

He begins to wonder if it’s true.

Sokka is seven when his mom dies. He remembers the last days at the hospital as a blur. He wishes the grown-ups would remember that just because they spell things out doesn’t mean he doesn’t know what they’re saying. He knows. _Cancer_ . _Stage IV. Terminal_. He knows what they all mean. He just isn’t ready for it. On the last day she pulls him and Katara up on the bed with her. He gives her butterfly kisses and tries not to break down and cry. He fails.

Zuko is eight when his mom leaves. He had heard yelling the previous night. And a loud bang. She comes to his room in the middle of the night to tell him she loves him, but she ‘just can’t live like this anymore’. The next morning her stuff is gone. Azula tells him it’s his fault. He was such a bad kid that she’s gone off to find herself a new family. But this time, for once, it seems to bother her too. Whatever. Azula always lies. 

When Sokka turns ten he starts apprenticing at the family business. He’s been helping out from behind the register for years. But it’s the first time his dad really takes time to show him the ropes. Inventory. Getting the best produce. Knowing what to keep in stock. How to prevent rowdy teenagers from stealing the merchandise. But his favorite part is the cash register. It sounds hopelessly nerdy, but he likes making change. Being able to beat the register. Not using a calculator to validate coupons and their regular sales. He’s at the cash register the first time he sees Zuko. 

He’s a pale, skinny kid with jet black hair. Sokka can see the car he came in parked outside. A black limousine. He’s never seen one of those up close before.

Limo-kid comes up to the counter and hands him a credit card, and a pack of aspirin. The aspirin is $2.50. They only accept cash for purchases under $5. 

“Sorry, dude. You’ll have to pay in cash.” Sokka explains, “It’s the policy.” 

“I don’t have any cash!” the kid snaps. He has golden eyes, Sokka’s never seen a kid with golden eyes. They’re kinda pretty. 

The kid looks rich though, going by the clothes, and the car, “Chill. Just pick something else. Once it’s over $5 I can take the card.” 

The kid looks towards the door nervously, then back at Sokka, “Okay. What would _you_ recommend?” 

This is a convenience store. Not a restaurant. Sokka can’t _recommend_ things. 

“Just take this.” Sokka grabs a red stress ball from their ‘impulse buys’ section, right under the counter, “Maybe you won’t get the headache next time.” 

The kid scowls, but takes it from his outstretched hand, he has such cold little fingers. 

Then Sokka takes the card from the kid’s hand, rings him up and swipes it, handing it back with the receipt. 

He’s out the door before Sokka has the chance to say his token, “Thank you, have a nice day!”

He doesn’t think much of it. Rich kids are all the same. 

When Zuko turns ten he starts getting stress headaches. It usually happens after a night of cramming for a test. His father’s condition for letting him stay in the soccer team was a B-average. Even though he was perfectly transparent about the fact that it _should_ be easy to maintain a B-average in the fourth grade, and the fact that Zuko struggles to is an utter disgrace. Soccer is his only solace, the only place where he’s actually the quickest and the fastest--so he’s anxious about losing it. English and history he manages to squeak through. Sometimes even with As. Even science. Every time, it just comes down to math. He hates it. And it hates him. 

He’s having a stress headache when he asks his father’s driver to pull over somewhere, anywhere, so he can get some aspirin. They’re in a strange part of town, and Zuko gets out alone. Father tells him he has to be quick, that he has important things waiting. He doesn’t say Zuko is not important. That much is implied.

He comes back in the car as fast as he can. Shoves the red ball in his pocket and gives it a squeeze. It actually makes him feel a bit better. He thinks of the kid at the counter. The one with tan skin and blue eyes. His smile. The warm brush of his hand. He feels a little flutter in his stomach. And a flush in his cheeks. But stifles it. The last thing he needs right now is something else that makes him different. 

Sokka gets his first girlfriend at twelve. Her name is Yue. And she’s soft-spoken and kind and _perfect_. They don’t do much, just walks to the park. Hanging around the Stop & Shop. Going to see movies when their pocket money allows it. She lets him touch her soft hair. They share their first kiss near the old train tracks. He’s devastated when she moves away. 

Zuko doesn’t date until thirteen. Living with Azula doesn’t really give you the best opinion of girls. He sees Mai for the first time at his father’s company party. They meet each other's eyes when his father is toasting the company for a proud fifty years. He decides that he likes her when she yawns during the dedication of his grandfather’s commemorative statue. They sneak off to the roof to complain about how boring these sort of parties are and how much they hate being there. When she leans in to kiss him at the end of the night it’s the happiest he’s ever been. They date until well, when _it_ happens. 

‘It’ is the culmination of every argument he’s ever had with his father. This time, it’s about having to repeat the seventh grade. Or to be more specific, repeat seventh grade math. He’s passed everything else. He’s ashamed, and angry already. He can’t take much more of this. His father keeps going on and on about how people will talk. How his son will make him a laughingstock. Zuko always hated math. He wants to finally say it. 

“Math is stupid and it doesn’t even matter!” he yells. 

Azula looks up from her book, because things just got interesting. 

“HOW DARE YOU RAISE YOUR VOICE TO ME?!” 

Zuko knows that look. He’s seen it before. But now his mother’s not there to save him. No one is. 

The last thing he hears is “You will learn respect. And suffering will be your teacher.” 

His father grabs him and pulls him towards the stovetop. It's on. The next part is just pain. He wakes up in the hospital a week later. His uncle is there. And he can’t see out of his left eye. At all. The left side of his face is red, swollen and burnt. Wrapped with bandages. There’ll need to be surgery. Or _surgeries_. To fix it. His father will pay for it all, in return for Zuko claiming it was an accident.

The scar never heals.

He lives with his Uncle after that. Or, to put it more correctly, he’s asked to stay with his Uncle until he can prove himself a worthy heir, intellectually, to the family company. In other words, prove that he isn't, as his father would say, a "common moron". He spends time listing out the ventures he could pursue to do so. But they’re all ridiculous and far-fetched. For him that is. Win the math olympiad. Publish a paper. Get into MIT. He’ll never get there. And with the whole thing with his eye, so much for soccer too. He starts taking his classes online. He really doesn’t want to be known as ‘the kid with one eye’ for the next four years. Uncle allows it.

At sixteen, Sokka gets the highest score in the entire school--a school full of the best and brightest--in the National Mathematics Contest. Beating out kids in higher grades. And taking a hearty lead over another girl in his year, one Azula Sugita.

He’s approached after the award ceremony by an elderly man, who says he’s Azula’s uncle. Which is weird, since she seems repulsed by him.

“Congratulations, young man. It is a fine accomplishment.”

“Thank you. I didn’t really expect this. Ya know?” Sokka can practically feel Azula’s glare boring through the back of his head.

“Do you ever tutor other students? With your talent, it would be a shame not to share it.” 

“Not really? I work at my dad’s store after school most days.” 

“My nephew needs some guidance in the subject. I would try to teach him myself. But for one reason or another. I have not been able to reach him.” 

Sokka imagines a stubborn little kid. Little kids hate math. That’s to be expected. They hate it even more when some family member, like a stubborn Uncle, tries to force it on them. 

“I really don’t know though.” Sokka explains honestly, “I’m saving up for this car. My dad lets me keep the tips when I work at the store.”

“Oh. I can provide some financial compensation. How do you feel about a hundred dollars an hour?” 

“A hundred...what--are you serious?! I mean. In that case. I’d be happy to. See what I can do.” 

Azula sneers at him on her way out, “Good luck. Zuzu’s hopeless.” 

Zuzu, huh, Sokka thinks to himself, that’s a weird name for a kid. 

* * *

“Uncle, I don’t need a tutor.” 

“You will like this one.” Uncle Iroh assures him. 

“Why?!” 

“He bested your sister.” Uncle chuckles, “That has to count for something.”

Zuko won’t lie, the idea of Azula going down does give this guy a point in his book, just one though. 

“This is your final year. You need to pass calculus. He could help you do that.” Uncle continues. 

“I can pass by myself.” 

“He is coming over in ten minutes. Look presentable.”

* * *

_Differential, Session 1_

Sokka has to take three buses to get here. It takes a full hour. They’re in the gentrified part of the city. The building where he was asked to show up has a doorman. And a guy that stands in the elevator with you and presses the button for you. In order to even get in he has to say that he has an appointment with the Sugita family. This is sooooo cool! 

The old man opens the door and asks him to come in. That his nephew is just in the other room. The walls in this place are all this rich burgundy. The accents gold. Traditional Japanese furnishings everywhere. It’s nice, if a bit, well, intense. The first thing Sokka sees when he enters the other room is the back of this kid’s head. Jet black hair. He’s much, much older than what Sokka thought he would be. He’s Sokka’s age. Or just a bit older than that. 

He’s sitting at a fancy, carved wooden desk, his back to Sokka. Not even turning around to acknowledge him. Rich people, Sokka sighs, I tell you. 

“Hey.” Sokka says, “Are you...Zuko?” 

“Yeah.” 

Cool, still not turning around. Okay. 

“Hey can I talk to you? I’m here about the math.” 

Zuko sighs and turns around. The first thing Sokka notices is that oh shit, he’s _pretty_. All soft black hair and sharp golden eyes. There’s a softness and hardness about him all at the same time. The second thing he notices is that scar. Because like. It covers half his face. And it looks painful as hell. The third thing he sees is the red stress ball in his hand. Sort of like the ones they sell at the old Stop & Shop. 

“Wait. Let me see that.” Sokka comes closer. 

For a few seconds, it seems like Zuko thinks he’s talking about the scar--cause of his expression of pure terror, but then Sokka takes the ball from him. 

Yup, small ‘S&S’, in little white letters. He smiles at Zuko, “You sir, are a valued customer.” 

“I don’t know what you’re talking about.” 

“This. You had to have gotten it from my store.” 

“Your. Store.” 

“Weeeell. My dad’s store.” 

Zuko just stares at him, “You’re supposed to be him? My Uncle said you were some sort of genius. You sound like an idiot. How old are you, thirteen?” 

“Well you sound like an asshole. I'm sixteen. And a quarter.” 

“This is useless. Just show yourself out.” Zuko shows him the door. 

Sokka sees the calculator on Zuko’s desk. Thinks of a hundred dollars an hour. For weeks on end. And thinks of the sweet, sweet car that will sit in his driveway. 

“Before you let me go. Wanna see a trick?” 

“No.” 

“Ask me to multiply any two numbers. And I’ll get the answer faster than you and that calculator.”

“...Four hundred twenty-one. Times thirty-seven.” Zuko picks up the calculator.

“Fifteen thousand, five hundred seventy-seven. Come on. Think bigger.”

“Three thousand four-hundred fifty-six. And Four thousand seven-hundred eighty-six.”

“Sixteen million. Five hundred forty thousand four-hundred and sixteen.” Sokka smiles, sometimes, it’s good to be him. 

“One million. Six hundred and forty seven thousand. Eight hundred and ninety-four. That. Into One million. Three hundred and forty five thousand. Eight hundred and thirty-seven.” Zuko says this last one confidently, thinking he finally has him. 

This one, honestly, does strain him a bit, but, “Two trillion. Two hundred seventeen billion. Seven hundred ninety-six million. Seven hundred seventeen thousand. Two hundred.” Sokka pauses for dramatic effect, “And seventy-eight.”

“Uh. There’s no way.” Zuko scoffs, “No way.”

“Check it.” 

“I will!” Zuko looks down angrily at the answer displayed on the calculator, “This doesn’t prove anything. It’s just a party trick.” 

“Oh come on. Please. Let me teach you some magic numbers.” 

“Why do you want to teach me math so bad?!” 

“I need a car. I’m just a guy. Who can do math. And I don’t wanna share my mom’s old station wagon with my sister. I’m not gonna get that kinda cash working at the store.”

“Station wagons are still around?” 

“Stop it with the rich people privilege. Do you wanna learn something or not?”

"..."

"..."

“Okay, Grocery store. Show me what you got.” 

“It’s a _convenience_ store thank you very much.” 

* * *

_Differential, Session 2_

“You’re not ready to take the derivative of anything.” Sokka tries to break it to him gently. 

“What do you mean?! I passed pre-calc.”

“Your algebra’s a hot mess. You don’t have a feel for numbers at all. If you build on-top of this. You’re gonna crash and burn.” Sokka explains. 

“So you’re giving up already.” 

“We’re not giving up. We’re just gonna change our strategy. What are you good at?”

“I’m not good at anything.”

“Nobody is not good at _anything_.” 

“I am. I’m nobody.” 

“You’re funny.” Sokka points out, “That was sorta funny.” 

“I know what you’re doing. Trying to figure me out. Get to know me. And then once you get me. Or whatever. I’ll suddenly be good at math. Because I’ve been healed by the power of friendship. But that’s bullshit.” 

“Why should I get to know you? If anything, you should get to know me. I’m the one that’s good at math. And you wanna be.” Sokka grins. 

“Then why did you ask me what I’m good at?” 

“So I can figure out how to teach you. It’s not your fault you’ve never been taught correctly.” 

_It’s not your fault._ Now there’s something Zuko’s never heard before. 

“I’m not bad. At drawing stuff.”

This is a lie. He’s objectively exceptional at it. But Sokka doesn’t have to know that. 

“Okay. Then we’ll start with some pictures. And we'll start at the beginning.” 

* * *

_Differential, Session 3_

Sokka may be gifted at math. But he’s terrible at drawing. He’s filled up an entire chalkboard of circles and squares. And letters. Connecting things with a bunch of arrows. He’s decided to start at the very earliest beginning. The beginnings of algebra. Variables. 

He tries to liven things up by drawing animals once in a while instead of plain circles. 

“Is that...a cow?” Zuko squints. 

“It’s a bird!” Sokka circles it a few times, “See. Wings.”

“Those look like horns.”

“You try then, smarty pants.” Sokka tosses him the chalk. 

That’s how the evening devolves into Zuko instructing Sokka on how to properly draw animals. Pigs. Cows. Chickens. Ducks. Horses. Donkeys. Birds.

“Now this.” Zuko finishes his picture with a flourish, “Is a bird.” 

“I see no difference.” Sokka looks back at his own picture, which honestly, in comparison, is an abomination. 

“You see no difference? You see no--mine actually has wings!” 

This goes on for a while. And for a few blissful minutes. Math is forgotten. 

Sokka actually feels bad for accepting a hundred dollars for the session at the end--considering, so he tries to hand back $50, but Zuko’s Uncle just isn’t having it. So he gets on his way. 

* * *

_Differential, Session 4_

“Hey. How come you don’t go to school?” Sokka writes up the day’s warm-up exercises on the board. 

“Why do you think?”

“You’re so rich that school comes to you?” Sokka suggests, “You just hate the sight of us regular people?”

“Something like that.”

* * *

_Differential, Session 5_

“How long are you going to make me do algebra? Teach me the advanced set!” Zuko demands. 

“Yeah, that’s going to be a no from me.” 

“I’m bored.” Zuko pushes the paper away. 

“How can you be bored? This stuff is so much fun.” Sokka takes the paper from him, and starts making notes on it, “They’re like little puzzles.” 

“Fun? You think this is fun? This is torture!”

“Okay. Maybe we should take a little break. Get some Starbucks. Lighten up. Stop yelling at your tutor.”

“Anything to get away from this.” 

Zuko grabs a pair of sunglasses before they head out. When he puts them on, you can almost not see the scar. Just the edges of it. Sokka wonders how he justifies this when he goes out at night. Maybe he just doesn’t go out at night at all. 

He orders a black coffee when they get there and judges the hell out of Sokka’s ridiculous strawberry frappe with caramel drizzle. 

“That’s a stupid drink.” Zuko takes a sip of his, “Do you even know how much sugar is in that?” 

“Yeah? Enjoy your hot bean water. Sugar is awesome.” 

“You’ll just crash later.” 

Sokka smiles, “Totally worth it.” 

Sokka can't stop staring at Zuko. He looks so secret agent-like. With his broody look. And those sunglasses. Like he’s in here investigating a murder. Sokka wishes he could pull off a vibe like that. 

“Stop looking at me. I hate it when people do that.” 

“I was just thinking that you kinda look like a secret agent.” 

“...you think I look like what?” 

“Who else wears sunglasses inside?” 

“I’ve--I’ve never thought about it like that.” He takes another sip of his coffee, “...If I was a secret agent. Who would you be?” 

“Your contact. In the underworld. Duh.” 

“What are we discussing?” 

“Drugs?” Sokka strokes his chin, “Yeah. Drugs.”

Zuko leans in conspiratorially, “Maybe you’re turning against your boss. The kingpin.”

“And this Starbucks is where it’s all going down.” Sokka finishes the story.

"Yeah." Zuko gives him a little half-smile. 

They toss their empty drinks, and head back up. 

* * *

_Differential, Session 6_

"Okay. We're not going to get anywhere with this attitude." 

"What attitude? I don't have an attitude." Zuko insists, "Maybe you have an attitude."

"You hate math. And you'll never be good at something you hate."

"Even if I loved it. I'd still be bad at it."

"Maybe. But not _this_ bad." Sokka points out.

"But it's easy for you to love it! Don't you have like an IQ of a million?"

"161. But that's not the point. I loved it before I even knew I was smart. Before I knew I was good at it."

"Don't tell me a personal story that you think is gonna make us bond." 

"Too late. I liked counting things a lot. As a kid. Do you ever count stuff?" 

Zuko looks confused, "What are you talking about? Everyone knows how to count."

"Yeah. Yeah. Everyone knows how. But they don't do it. Okay. What do you think about when you look at something?"

"It'd be really nice if I could see this shit out of both eyes."

"Okay, smartass. Other than that." Sokka guides him along. 

"I guess I see where stuff is. How big it is. Colors." 

"But not how many. How many things there are. How many of each kind. Coincidence? I think not."

"How will this help me with calculus!?"

"Just work with me here, okay? Just try thinking that way. Just for some fun."

They take a walk. To put this theory into practice. Zuko dons his sunglasses again. This time, they’re Ray Bans. Which Sokka knows, are like $200 sunglasses. Fucking rich people. 

"We'll start with birds. Since you're such an expert."

"I'm not an expert. You're just. Really bad at drawing them."

"That cuts deep, Zuko." Sokka gestures to the pigeons gathered across the street, "Just tell me a number."

"I don't know. Seven."

"There's fifteen. You're only seeing half."

"Maybe you're seeing double!"

They walk a little further. And Zuko thinks of a more interesting way they can play this game. A way that will distract Sokka. From asking _him_ these stupid questions.

He points back at his own building, "How many stories?"

"Sixteen." 

When he gets to the cross walk, he asks, "How many steps to the other side?"

"Twenty-five."

Zuko takes comically large steps just to prove him wrong. 

They get all the way to the park in the center of the city. Sit down on a bench. And watch the ducks. 

This time, Sokka asks the question again, "How many ducks?"

"There's six. And four ducklings."

"That's...right. Hey, nice!"

Zuko just shrugs "I used to come here a lot."

"Wanna know some cool things about math?" 

"Okay."

"Take any number. Multiply it by three. And add the digits together. The sum will be divisible by three!" 

"That's not that cool."

"Okay. Okay. Try this. Do you know what a hundred and eleven million. A hundred and eleven thousand a hundred and eleven is. Times itself?"

"I think you're the only one who knows that." 

Sokka types it in on his phone, the answer that is, and shows it to him. 

12,345,678,987,654,321.

Zuko just stares at it. 

"It goes backwards and forwards. It's amazing!" 

"I guess."

Sokka sighs, "Okay. I'm going to show you something that's very near and dear to my heart. So you can't shit on it. It's my favorite equation. And it stands for love. And everything that's good in this world."

_God you're weird_ , Zuko thinks to himself. 

"There's a number called _e_." Sokka explains, "It's actually a limit. And we'll get to it later. But for now just remember that it's a really important number. And it's irrational. Which means if you write it out as a decimal it's just long as fuck and doesn't really havd a pattern to the digits."

"Okay." 

"Then there's a number called _i_ , it's the square root of negative one. So it doesn't actually exist. Then there's _pi_. Which I'm thinking you know." 

Sokka takes a small piece of paper out of his pocket. It’s a receipt from the Stop & Shop. He fishes a pencil from his backpack. Cause yeah, he's been walking around this whole time with a school bag. _What a fucking nerd_. 

He writes the equation on the back of the receipt. 

_e^i * pi + 1 = 0_

"This is love. This is life." Sokka says, "All of these numbers are crazy by themselves. Except one. But. You know. Then you mash them up together. And you get zero. Can you believe it?! This is the world making sense of chaos!"

He puts it in Zuko's hand, "I'm giving it to you."

_This is love. To him. And he's giving it to me._

"Why?"

"One day. You might appreciate it."

* * *

_Differential, Session 7_

Zuko's basics have gotten better. Sokka can tell. And why are basics important? Because you can't do complicated shit if you're still second-guessing yourself on the easy shit. And now, well, he's not guessing as much. 

He gets through Sokka's warm-ups in record time. And Sokka feels all warm and proud. His first student. 

"Great. This is great. You really did a good job." 

"This is like. Seventh grade math." 

"But you killed it!" Sokka says happily. 

_I'd like to kill your optimism._

"I think you've earned a little reward." 

"You're going home?" 

"I'm gonna pretend I didn't hear that. Get out your sunglasses. We're getting ice cream."

Once again. There's an immense sugar disparity. Zuko gets plain vanilla. A single scoop. Not even in a cone. And Sokka gets some multicolored monstrosity with sprinkles and cream. 

"You're going to get diabetes and die." Zuko announces. 

"Don't be rude! And don't knock it till you try it."

"I'm not trying that."

"Come on. Just a little bite?" 

He takes his spoon over there and scrapes off the tiniest bit. Then tastes it. _Disgusting._ So sweet. And wait. Fruity. That's kinda nice. 

"I hate it." 

"Sure you do." Sokka takes a larger bite. 

"Why do you never show up on time?" 

"Hey. I take three different buses to get here. It adds up."

"That's stupid. I could just send the car for you."

Sokka tries to imagine a car like the one Zuko probably means pulling up to the Stop & Shop. It's only happened once before. As far as he can remember. 

"Why don't you just come to me?" Sokka asks. 

_Come to him?_ Zuko hasn't left the ten block radius around Uncle's building in years. 

"I can't." 

"Don't you wanna see The Stop & Shop? It's only the second-best place in the world."

“What’s in it for me?”

“I’ll let you make change.”

“Not helping.” 

“What about an I O U. You can collect later.” 

Zuko considers it’s always nice to have someone in his debt. The Sugitas have made their fortune by having people in their debt. Besides, maybe it would be nice to get out of here. Just once. 

“Okay. I’ll come.”


	2. Differential II

_Differential, Session 8_

Zuko comes exactly on time. He’s nervous, and he has his stress ball in the pocket of his jeans just in case. Sokka’s beaming when he meets him at the front of the store. 

“Prepare to be amazed,” Sokka says and then pulls him inside. They zoom through the chips aisle. The beverages freezer. They pass the cotton candy machine and a popcorn machine, even a little spinning display with taquitos. 

Zuko does a little nervous gasp as Sokka takes his hand and yanks him in front of what is clearly a very important shelf. At first all Zuko sees are magazines. He tries not to concentrate on the sudden point of contact between them. 

“I got my dad to add a comic book section,” Sokka says, “Now it’s not a particularly big seller during the winter months. But it really takes off during the summer when the grade school demographic starts showing up. You know, nothing to do, other than the ones that have summer camp, but you don’t have many of those around this neighborhood, you know, typically pretty expensive those types of things, and a book is just about as much as a pack of gum. So for the money you’re probably getting more entertainment...” 

Zuko doesn’t know what to say about this, since he doesn’t really know much about convenience stores, their demographics, or comic books, since they weren’t really allowed at his house growing up. So he just looks at Sokka, who is still talking, then realizes that it’s even more awkward if he says nothing. 

“Great,” Zuko settles on finally, as Sokka’s train comes to a halt. 

Sokka rolls his eyes, “Don’t pretend to be interested if you’re not.” 

“I’m not _not_ interested, I just don’t read comics! I don’t know what’s so great about them!” Zuko snaps, a little defensive. 

“Hey, if you wow me in today’s session I just might let you take a copy for free,” Sokka smiles. 

Zuko sighs, “I know what my Uncle is paying you. With that kind of money I could--” 

“Yeah, yeah, rich jerkboy,” Sokka rattles on, taking Zuko’s hand again and spiriting him away upstairs, “With that kind of money you could buy this store. The block. Maybe even the entire street! But it’ll mean more coming from me, as a reward than bought with cold hard cash, trust me.” 

“You’re not having any problem taking cold hard cash to teach math to an idiot,” Zuko huffs, as they arrive into what he assumes is Sokka’s family’s personal apartment. 

Sokka pauses his prattling for the first time, and he looks at Zuko sort of curiously. It’s not a look of pity, for which Zuko is infinitely thankful. 

“I don’t think you’re an idiot,” Sokka says, slowly and very definitely. 

“Idiot, bad at math, same difference.” 

Sokka smiles from ear-to-ear, “Dude, I’m a _genius_ at math. My sister calls me an idiot all the time. S’not the same thing. Now come on, as my dad says, this house isn’t for moping.” 

Zuko follows Sokka into a small room with two beds. 

Sokka explains the sleeping arrangements really quick, “This used to be mine and Katara’s room. But then she went and became a girl and needed space to do girl stuff away from me. So now, she and gran-gran sleep in the big bedroom. Me and dad sleep here, unless he’s out of town. Then he sleeps wherever he is. He’s out of town on Wednesday and Sunday nights, coordinating shipments. We have a lot of direct relationships with people who grow their own food, it’s why our limited selection of produce is so fresh.” 

“Oh,” Zuko looks around. It’s a rather small room. The paint is baby blue, and chipping. There are a few pictures fastened on the walls with push-pins. One of Sokka and a girl with brown red hair and a sweatshirt tied around her waist. One of a much younger Sokka and a woman that kind of looks like him. She has his easy smile. 

Zuko cocks his head towards the first picture, “um, girlfriend?” He doesn’t know why he asks. Maybe he’s just trying to kill time so they spend less of it doing math. 

But that doesn’t account for the slight relief he feels when his impossibly annoying tutor shakes his head and says, “no, not my girlfriend. Just a girl, who’s also a friend. We met at math camp.” 

_Of course they met at math camp._

“Why am I not surprised?” Zuko shakes his head. The derision on his face must be clear. 

“You know you’re kind of an asshole, just because you suck at it doesn’t mean you should knock it. Math is personal to me,” Sokka says, and the way he says it is the only reason why Zuko doesn’t get very, very upset about it. 

Sokka’s voice is kind. The way he says every sentence is overly animated and so, so expressive. It’s not meant to be mean. Nothing he says is meant to be mean. It’s usually difficult for Zuko to figure out stuff like that, what people mean when they say things. So he usually assumes it’s not meant well. But with Sokka he finds himself doing the opposite. 

Sokka ruffles around in a drawer for a second, then pulls out a workbook, “I think you’re ready for limits.” 

“Limits?” Zuko asks, chewing on his own bottom lip. 

“Yeah, limits, now shut up and listen before you reach the limit of my patience,” Sokka says as he thumbs through the book. 

Zuko checks that there’s no one else in the house by turning his good ear towards the door. Then, satisfied that there’s no one here but Sokka, takes off his sunglasses and puts them by the desk. 

“Ha,” he laughs mockingly, “Very funny. Show me what you got.” 

* * *

_Differential, Session 9_

Zuko is better at limits than he was at algebra. Sokka is pleased. He does claim some of the credit of course, because cleaning up Zuko’s algebra was no small feat. But he has to admit, most of the turnaround was due to Zuko alone. He’s not resisting Sokka any more. He’s not actively trying hard either. But, baby steps. 

Sokka has a green chalk board and some white chalk he uses as he explains the concepts. Limit as x approaches 10. Limit as x approaches 35. Limit of a function at a point, approached from both sides of the point, from negative infinity and positive infinity. He briefly waxes poetic on the concept of infinity itself, before he realizes he’s lost Zuko somewhere and comes to a stop. It’s not the first time something like that’s happened. 

“Why didn’t you tell me?” Sokka asks carefully. 

“Tell you what?” 

Saying this could be a huge mistake, but Sokka wants to know, “I was saying something, and I could tell that you weren’t following along. But you acted like you were.” 

“I was following along!” Zuko says, and there’s a hard edge to his voice that wasn’t there before. 

So maybe this isn’t the time to press the point. Especially since Sokka hears voices. Footsteps on the stairs too. It must be Katara. Sokka glances at the sunglasses that were set aside on his desk. He’s not sure what exactly the deal is with those, but if he had to guess, it seems like Zuko wears them around most people. He had very conspicuously waited until they were alone before taking them off earlier. Sokka noticed. He makes a quick calculation in his head. And he takes the glasses and puts them on a stunned Zuko’s face a split second before Katara arrives.

“Sokka have you seen my green leggings anywhere?” Katara asks, leaning against the doorframe, “Oh. Um, who are you?” 

“Zuko,” Zuko answers. It’s as good an answer as any. Not particularly descriptive, but to the point. 

“Right, I’m Katara, and from the look on my brother’s face...I'm interrupting something, let me know if you see my leggings okay!” she says as she leaves. 

“Yeah, fine,” Zuko says in reply. 

“She was talking to me, don’t worry about it,” Sokka points out. This time he shuts the door. 

“You didn’t have to,” Zuko takes the sunglasses off one more time, “Usually, it’s just. Well, I try to. If it’s someone I’ll only see once or twice there’s no need. But if your sister’s gonna be around a lot, I should probably just not wear--you should have told me she was coming!” 

Sokka realizes several things in that moment. First, Zuko didn’t seem to realize she was there until the second she made her appearance in that doorway, even though she clomped up the stairs as if she was wearing horseshoes. He was facing Sokka, with his scarred ear towards the door. He didn’t hear her coming. Second, Zuko doesn’t perform well at math when he’s flustered like this. They’re not gonna get anywhere tonight if he’s not in a better mood. Third, Sokka had some non-tutory reasons to want Zuko here in his room, in his house. With all the studying and the working that he usually did, he hadn’t been able to just hangout with a guy in ages. He's wanted to. 

“I’ll tell you next time, promise,” Sokka puts the book about limits back in the drawer. “Wanna play some soccer while it’s still light out? There’s a field near my old school. I know it’s just us, but I can be goalie, and we can see if you can get any past me.” 

Zuko’s eyes brighten up like anything and there’s a wave of warmth in Sokka’s middle. 

“If you’re ready to lose,” Zuko shrugs, “Sure.” 

The field is just minutes away, and Sokka finds himself counting things the second they get outside. He does the familiar count of the store inventory at a glance. Then counts cracks in the sidewalk, the number of posters on the bulletin board behind the cash register, and open parking spaces in their lot. 

Zuko doesn’t seem to mind walking in silence. Sokka watches him put his hands into his pockets and fall into step beside him. He finds himself counting Zuko’s breaths. The number of times his fair falls in front of his face. The number of times he bothers to push it back. He does so around forty five percent of the time. Idle thoughts like these don’t usually take up much of his headspace anymore. They’re always just there, a background thread of calculations, whirring softly in the backroom of his brain. But these are distracting enough that he can’t focus on the graph theory problems he’d been working on in his free time, breaking apart in his brain. 

He thinks about the different variations of his own name in Zuko’s voice. Changes in tone, pitch, and manner. How they each branch and predict his mood. It’s interesting. He likes the way the sounds feel in Zuko’s mouth. 

“Where’s this field of yours anyway?” Zuko asks, breaking into the theories in Sokka’s head and snapping him back into reality. 

“Not that far, dude, we’re almost there,” Sokka assures, “When do you have to be back?” 

“Never.” 

“No, seriously.” 

“It’s not like anyone cares how late I come home, Sokka.” 

Sokka thinks about Zuko’s Uncle. Zuko’s Uncle would probably care.

“I don’t think that’s true, but I’m not gonna argue with you right now.” 

“Thank you.” 

When they get to the field Sokka grabs a ball from a padlocked bin on the side of the court. The code’s still the same, and his dad is friends with the coach, Bato, so he doesn’t think it’ll be a problem. 

He approaches the goal, “You wanna defend or…?” 

“I already said I’d be okay with you playing goalie, just kick it to me.” 

Sokka does. And then it’s on. Zuko is quick, he’s fast. The first one Sokka doesn’t even see coming. One point to Zuko. The second one Sokka sees, but it whizzes past him just the same. The third one Sokka blocks with a swift kick with his right leg. _Easy._ Zuko shrugs as if he just got lucky. He wastes no time coming back with a hit that goes over Sokka’s head right into the net. 

They play for at least a half hour. Maybe more. Final score? Sokka doesn’t wanna talk about it. 

He takes a seat on the grass next to Zuko, and bemoans the fact that he didn’t remember to bring any water over here. 

Of course Zuko is sitting there, barely a foot away, practically glowing. Getting this many goals on Sokka was a win. Winning looks good on him. His hair is a little sweaty, and a single bead of it drips down his cheek. Sokka follows its path down Zuko’s neck until it creeps under his t-shirt. _Whoa._

“Go ahead, gloat at the expense of Sokka,” Sokka laughs nervously. 

“Good game,” Zuko extends a hand to him. 

Sokka shakes it, “Wasn’t really a game, but I feel you, good game to you too. You were really great.” 

Zuko laughs again, but then his happiness goes away like a switch. 

“It doesn’t matter.” 

“Who told you that?” 

The look Zuko gives him could burn through steel. 

“Fine, fine, sorry I asked.” 

Sokka’s still counting Zuko’s breaths. They’re quicker and shallower now. Sokka’s hand falls lightly to his wrist to take a pulse. Fast, much higher than it should be. He’s anxious. He’s a shade paler than before too. 

“I stopped going to this school when I was like five,” Sokka explains, letting go of Zuko’s wrist. 

“I barely remember the place,” he goes on, “but I still miss it.” 

“Why’d you change schools?” 

“I had this teacher, Miss June, she realized that I was smart. She thought I could really go places, I guess. I never said no, especially since everyone seemed so proud of me. But I never wanted it. Yeah, I know, I know. Boo hoo hoo for Sokka, he’s so smart but doesn’t want to be. I know how it sounds. I don’t wanna be a jerk.” 

“No, I get that. You didn’t want to, but you knew it was the honorable thing to do.” 

Breath in. Breath out. Sokka notices Zuko’s breaths slowing down. His own are picking up a bit, but that’s not the point. The average of their heart rates is pretty steady. 

“I’ve never used that word to describe it, but I guess so?” 

“Isn’t it nice though, just having stuff come easily?” 

“Not everything comes easily,” Sokka chuckles, “You should have seen me trying to flirt with my first girlfriend Yue. I asked her if she wanted to do an activity with me. Seriously! I asked her that. I was so stupid! She was nice about it though.” 

“What happened to her?”

“She moved away.” 

“Oh. Sorry about that.” 

“You left your school too, right?” Sokka asks cautiously. 

Zuko doesn’t answer, and just remains there, with his knees pressed up against his chest. He’s chewing on his lip and looking at his shoes. Sokka hasn’t known him very long, but he’s worried about him. Sokka also can’t break life and math apart in his own mind. They’re linked so strongly. So if Zuko has barriers up about life, he definitely has them with math. 

“Look, Zuko. You don’t have to talk to me about anything. But I do want to know what you’re thinking. Otherwise I can’t help you. Just, trust me. There’s no one here who’s gonna judge you for it. Especially not me.” 

For a moment, Sokka is sure he’s going to get yelled at. 

But Zuko answers the question, “Yeah, I did leave my school too.” 

It’s not much of a response. But Sokka’s not pushing. 

* * *

_Differential, Session 10_

Zuko spends time on the practice worksheets. Sokka had emailed them to him late the night he got home. He had fully intended to ignore any practice worksheets that weren’t explicitly about calculus, since he’s been feeling kinda awful about the fact that he’s practicing math that thirteen year olds already know. But he wants to do well on these all of a sudden. 

Sokka also sends him a bunch of scans. They’re all visualizations of limits. Sokka’s drawn what must be dozens of interpretations of the same thing. The text of the email just read ‘you’re a visual learner right, hope these help :)’. They do help. 

Every problem Zuko does he remembers the small pat on the back he sometimes gets when he does a problem right in their sessions. Sokka’s smile, egging him on. He likes that it doesn’t go the other way. Sokka never gets disappointed when he gets one wrong. So Zuko feels free to just try in front of him. 

It had never been like that, even with Uncle. It’s not like Uncle gets disappointed either, when he’s tried to help Zuko with math. But Zuko cannot shake the urge to act like he knows exactly what he’s doing at all costs. Even to the detriment of learning things the proper way. He can’t show Uncle that he doesn’t get it, because Uncle’s already been so kind letting him stay in his place. Taking care of him all these years. It’s different with Sokka. Sometimes Zuko can pretend they’re just friends studying together. Sokka and his jokes just have that effect on him. 

After the problems are over he finds himself doodling on the scratch paper he got out. He draws a soccer ball first. The goalpost. The field. Then he stops and scratches it out. He rips the paper to pieces. 

**Notes for the Chapter:**

> super late update, but i finally have the brain juice to keep writing this! and im excited  
> im at @bluberry-spicehead now :)))


	3. Differential III

_Differential, Session 11_

“You practiced,” Sokka notes, going through the worksheets. “This is really good, you’re improving.” 

Zuko just brushes it off. “It took _way_ too long.” 

“That doesn’t matter, what matters is the process. Once you do things the right way, step by step. You’ll be able to pick up speed later. Trust me.” 

Sokka looks at him, and really wonders what it would take to get to that. Real, honest trust. What would it take for Zuko to get that his assessments and his praise are sincere? Sokka’s mathematical mind has several theories, each with projected rates of success. But he doesn’t want to play those types of probabilistic games. Not with someone who’s clearly been told they’re bad at this, many, many times before. He wants to gain Zuko’s trust the right way. The human way. Not by calculating for it. 

“What are we doing today? Derivatives I hope,” Zuko mumbles, sitting down on Sokka’s bed. There’s a hopeful gleam in his eye, and Sokka hates that he has to crush it. 

“Nope, no can do.” Sokka grabs some graph paper from his desk. “It’s geometry time.” 

Geometry, with its lines and curves. Artistic symmetry and patterns. This at least should come to Zuko more easily. Sokka figures he’ll see it, the meaning behind the series of points, just like he does when he sketches things. If he’s good at this, if he gets it, he’ll get a little confidence. Then the rest of the day will go smoother. Sokka’s sure that all Zuko needs is a little confidence. A little faith. And all Sokka needs is to be the one that helps him get it. As a tutor of course. Tutorly duties demand it. 

Zuko takes the graph paper from him, and writes his own name on the top left corner. 

“Uh, you don’t need to do that unless you want to?” Sokka glances over at the signature. 

“Oh, I- well how will you tell that this is mine, compared to all of your other students?” 

_Okay._ Well. That’s...interesting. So Zuko thinks that he has other students. That he has in fact taught math to people before, one-on-one. This is unfortunately not true. It’s quite awkward. Sokka doesn’t know how Zuko will take it, but he decides to bite the bullet anyway. 

“You’re, kind of the only one,” Sokka admits. “I don’t have any other students.” 

“Oh.” Zuko looks away. He exhales deeply. He clenches his fist. 

“Is that a good oh? A get-me-out-of-here oh? What are we working with here?” 

“No that makes sense, with a problem like this, like me, it requires a thpecialist,” Zuko says, and Sokka can tell with the way he lisps the last word that he’s getting nervous again. 

“A what?” Sokka asks, because he doesn’t quite get what kind of problem is being solved here. 

“You know what I meant to say. Or are you gonna make fun of me for that too? I looked you up!” Zuko snaps. “I looked you up. I’d done it before, but this time I actually glanced at some of the articles. You’ve done research with college professors. You’re way, way beyond this kind of geometry. A _normal_ calculus tutor wouldn’t be able to help someone like me. It had to be you. And since you don’t have any other students...” 

“I’m not, I’m not making fun of you. I just want to know what’s wrong, I’m really confused here.” 

“You’re the genius, don’t make me say it,” Zuko says, hurt now, instead of angry. A crazed part of Sokka wants to risk it all and hug him. He doesn’t. Because he still doesn’t _quite_ know what this is about. Why is Zuko upset? _Why is Zuko upset?_

“Please, whatever it is, you can tell me.”

“No.” 

“Zuko.”

“Let’s just move on,” Zuko says, “I-I don’t even know why I brought it up. Just-” 

“Okay,” Sokka says, and he sets his hand briefly over Zuko’s, “It’s okay.” 

Zuko’s eyes widen at the contact, but he just nods. 

“Functions,” Sokka says, “We’ll start with functions.” 

Sokka enjoys showing him his favorite functions. He tells him points to graph and asks Zuko to guess the shapes and lines they will form. He leans over Zuko’s shoulder and guides his hand drawing a perfect parabola. Hyperbola. Ellipse. Zuko’s hand is soft and warm underneath his, and it’s sort of hard to even let go. Sokka tries his hardest to focus on the patterns of graphite and not on the other boy’s face. Zuko’s focusing very hard on the graph paper. 

Even right now, with the tension between them, Zuko still has that urge to please. Sokka continues to wonder what the problem was. 

He explains tangent lines, secant lines, the area of a circle, rectangle, parallelogram. Zuko doesn’t complain that it’s kid stuff or that he’s too old for it. But he still seems hurt. Sokka aches to know what his earlier outburst was about.

“Did my Uncle ask for, uh, progress reports or anything?” Zuko asks with a forced nonchalance. 

“No, nothing like that.” 

“Oh.” 

_Uncle._ This is somehow about Zuko’s Uncle. The gears in Sokka’s brain grind furiously, then come careening to a halt. There’s a wild pull on the strings of his heart. And then he gets it. 

Sokka has had time to see it for himself. Zuko’s need to do well. The fact that he’s reluctant to admit when he doesn’t understand something. Appearing ‘good’ at math is important to him, or someone clearly told him that it mattered. Now that Zuko knows that Sokka doesn’t teach anyone else. Zuko thinks his Uncle thinks that he’s stupid. Because why else would he pick someone like Sokka, someone ‘gifted’ (god does he hate that word) to teach him. Sokka’s a special solution for a special problem. At least that’s how Zuko sees it. 

_I don’t see you as a problem._ Sokka wants to tell him. He’s a person, one that Sokka genuinely likes. Sure Sokka will think things through about him in order to figure out how to make him feel comfortable, but it’s never been about fixing him. 

“Your Uncle seems like a nice guy,” Sokka says. 

“He is.” 

“He seems like he cares about you a lot.” 

No answer. Only the sound of graphite on paper. 

“Then I don’t think your Uncle approached me at that math contest because I won it,” Sokka says. 

“What?” 

“He didn’t think you needed someone who could win math awards to teach you because you’re--whatever it is you’re thinking.” 

“Then why?! Why you? My uncle doesn’t even know you,” Zuko says softly. There’s a guardedness in Zuko’s expression. Like he’s preparing to be let down. Or expecting Sokka to be mean to him. It cuts deep to Sokka’s core and thinks very, very carefully about what he says next. 

“...Maybe he saw how nervous I looked alone on that stage. Even after I won. Like I didn’t deserve to be there. Because honestly? I don’t really know that I do deserve it. So, what I’m trying to say is, I think that he thought we could understand each other?”

“You think that?” Zuko asks quietly, turning towards him, looking up from the paper, his brows furrowed in concentration. Even amidst the strain this conversation is causing him, Sokka has time to find it sort of cute. “I mean, I don’t get it though. Why wouldn’t _you_ deserve what you’ve got?” 

“I work part time in a grocery store, remember? Yay for grocery boy. He can divide fractions in his head!” Sokka does a half-hearted cheering motion. 

“Ah. Right.”

“Yeah, ah. I go into everything having something to prove and even if I win, it’s just--”

“Not good enough,” Zuko finishes. 

“Yeah,” Sokka sighs. “Yeah. Also, I really do mean it. You’re getting a lot better every time we do this.”

“Well you’re the expert.” 

“I am, I have the research credits to prove it,” Sokka grins, “What else did you get when you internet stalked me?” 

“Not much, you’re a nerd.” 

“Ouch. I’m gonna need some ice for that burn.” 

Zuko laughs and the sound instantly makes everything lighten. Sokka likes this laugh, it’s real. Even if it’s short and rather too quickly stifled. It’d be nice to hear it again, Sokka notes to himself. Nicer still to be the cause of it. 

Sokka continues to explain about volumes, and parallels. How things fit together to make bigger things. That’s all geometry is. He tries to desperately paint a picture in Zuko’s head of what this means. Something that he hopes will stick. 

For the first time, Zuko interrupts him, “Again.” 

“You want me to go over that part again--I mean, yeah. Again. Of course. So, the volume of a pyramid…” 

On the inside, Sokka’s practically glowing. This is the first time Zuko’s ever told him outright that he doesn’t understand something. It must have been hard for him to even say that one word. _Again._

Sokka could talk about math like this for hours. He’s always loved it and no one really lets him talk about it. Katara’s good enough at it too, but she shares his aptitude and not his love. Her heart’s somewhere else and always has been. Dad doesn’t have time, typically, to listen to Sokka be lyrical and romantic about numbers and the way they rule the universe. Sokka’s friends, back when he had friends, and time for friends, they didn’t really talk about math. But Zuko really listens. Sure, probably because he has to, since Sokka’s being paid to do it. Still feels nice though. Zuko has something of an intense stare. It takes a little bit to get used to, but afterwards it feels more like a warm spotlight than anything else. 

There’s something about Sokka and math he has a hard time explaining to other people. The closest thing to it is scissors cutting wrapping paper. There’s that moment while cutting when the scissors start to glide, and it’s one smooth motion rather than a series of straight cuts. That’s what it feels like when something just _clicks._ The path forward becomes clear, the numbers all come together. Sokka can see it happening, just a little, for Zuko. 

Zuko’s getting it. He can identify the graphs as pieces of conic sections, the visual part of his brain can match the two dimensional with the three dimensional right away. Sokka can feel it radiating off of him, pleasure at getting questions right. The rush that comes with pieces falling into place. 

They finish off with the equations that define each graph. Sokka’s careful to remind him not to memorize, but to really get a feel of what each part of the equation means, based on all the drawings they did. In every word he speaks he’s asking Zuko to trust him. Because math is something he knows, sure. But Zuko is something he knows too. A little more each time he teaches him. 

They’re sitting right next to each other now. Their knees brushing against each other under the table. Sokka continues to drill him, and he loves how Zuko falls into step. Point for point. Moment by moment. 

“You know,” Sokka says, “You can define art with graphs like these too. There’s the kind of art you make, sketches and stuff. That’s raster art. And that’s really cool! But if you have images defined by lots and lots of equations on a 2D plane, it can resize and still look good. That’s vector art.” 

“Maybe later, you could show me that?”

“Yeah, definitely.” 

“Thank you,” Zuko replies. That it’s for more than just the promise of showing him vector art is implied. 

**Notes for the Chapter:**

> i know its weird to advertise another zukka fic in the end notes of my own zukka fic, especially if its not by me, but i need you to know that @zukkababey (rachel) on tumblr is also writing a tutor zukka fic called The Midnight Sky so go check it out because clearly if you're here you like that concept skdjfldksjlkfdjlsk <333: https://archiveofourown.org/works/27167479/chapters/66351325


	4. Differential IV

“Katara, look at this,” Sokka says, his eyes widening at his laptop screen. 

“No,” comes the reply from somewhere on the sofa in their small living room. 

“Come on, Katara, please,” Sokka whines. 

“Is it a matter of life and death?” she asks dryly. 

He looks over to where she’s sleeping, face down on the sofa cushions. She’s probably just taken an exam, and now she’s taking some well-deserved rest. Yeah, she definitely has the time for this. 

“Yeah, life and death,” Sokka answers, scrolling down the page. 

She shuffles her way over and comes to a stop behind him. “What are you even looking at?” 

“Zuko’s dad’s thesis.” 

“Who’s Zuko, is that the guy you were tutoring the other day? The one with the sunglasses?” 

“Yeah, him.” 

Katara raises an eyebrow. “And now you’re stalking his dad on the internet?” 

“I was just browsing when I saw the name. It’s a pretty impressive conjecture, I’ve read through the paper once, it just doesn’t sit right with me for some reason.” 

“If it’s a conjecture that means he couldn’t prove it, there’s just a lot of evidence to believe it is true,” Katara points out. “It probably doesn’t sit right with anyone. It’s not like a theorem or anything.” 

“It’s not that.” 

“Then what is it?” 

“I think I could prove this,” Sokka squints at it, “Maybe.” 

“You could prove that he’s right?” 

“No, I think I can prove that what he’s saying is mathematically impossible.” 

What’s more, Sokka reasons, suspecting what he does about Zuko and his dad, he  _ really, really  _ wants to. 

* * *

_ Differential, Session 12 _

“So, big day tomorrow, huh?” Sokka asks. He’s practically giddy.  _ For fuck’s sake.  _

“It’s a quiz, Sokka. It’s on the internet. Practically open book.” 

“I know, I know. But it’s your first real assessment since I’ve been your tutor!” 

“I didn’t know this type of relationship had milestones.” 

“This is big for me! You’re my first student!” Sokka smiles. 

“Lucky. Me.” 

“Glad you see it my way,” Sokka flashes him a smile, and pointedly ignores his sarcasm. 

“So what are we doing today? Drills? Prep? To make sure I nail this.”

“I got us movie tickets.” Sokka pulls two out of his pocket. 

“You did what?!” 

“Listen,” Sokka puts a hand on his shoulder, and it’s not entirely unwelcome. “Cramming the night before a test that you’re already prepared for is just gonna stress you out. And you are so, so unbelievably stressed out as it is. You make  _ me  _ look chill.” 

“So I’m paying a hundred dollars to go see a movie with you.” 

“I used the money from our last tutoring session to pay for the tickets, so technically you’re paying eighty six dollars to go see a movie with me.” 

“Okay,” Zuko says suddenly, as the idea occurs to him that if he appears reluctant any longer Sokka quite possibly might change his mind. He hates the part of him that really wants to go. 

A few minutes later, with microwave popcorn from the Stop and Shop in his hand, Zuko settles himself into the family station wagon. The second Sokka turns the key, the faint sound of hip hop emanates from the speakers. It’s an older car. There’s a carseat in the back. 

“Sometimes I pick up the neighborhood kids,” Sokka explains, “Carseat used to be Katara’s. Mine before that.” 

“Oh,” Zuko nods, watching as Sokka turns his head over his shoulder and pulls into reverse. The car is stick shift. Zuko’s never seen someone drive stick shift before. 

“Do you drive?” Sokka asks as he pulls into the main road. 

“No,” Zuko answers. “I don’t have a license.” 

“I can and everything,” he continues, a little defensively. “It’s legal, even with my eyesight, I checked. I just don’t want to.” 

“Hey, if I could get driven around everywhere I wouldn’t drive either. It’s fine, dude.” 

“That’s not why.” 

“Okay,” Sokka says, glancing at Zuko briefly before turning back to the road. “Do you want to talk about it?” 

“No.” 

“That’s fine too.”

Zuko likes how steady Sokka’s voice is. For years Zuko’s developed a finely honed ability to tell how people are really feeling based on their tone. He can look for disgust, and he can recognize disappointment. There’s none of it in the way Sokka talks to him. He lets out a breath he didn’t realize he was holding. 

“I haven’t been to see a movie in a theater in--I don’t even know how long it’s been.”

“Oh, me either,” Sokka admits. 

“Really?” 

“Yeah, really. Do you know how much it costs to see a movie these days? Besides, if I ever get the time there’s always YouTube, I never go to the movies,” Sokka shrugs, his eyes still fixed on the road. 

“Then how come--why are we going to the movies, Sokka.” 

“I’ve seen you do problems, okay? When you’ve got something figured out, and there’s no pressure, you’re fine. If I start timing you, you--” 

“I choke.” 

“I didn’t want to say it like that.” 

“When you go in to see a movie, for a few moments you’re not thinking about what goes on out here. Or in there,” Sokka points to Zuko’s head. “You’re thinking about what’s going on in the movie. It’s immersive.” 

“So?” 

“You’re good at things when you get immersed in them. When you draw stuff, it’s like I’m not even there. Which is very rude by the way. Or even when you do math, sometimes. When we’re just working things out, just talking and stuff. You’re really good.” 

“Okay, so this is practice to get immersed in something.” 

“Yeah, partially.” 

“What else?” Zuko folds his hands in his lap, and glances to the side once, to make eye contact with him.

“Like I said before, I don’t want you to be stressed out.”

Zuko puts on sunglasses before getting out of the car. It’s quite a sunny day, so for once he doesn’t feel that weird about wearing them. He has tried it both ways though. He gets  _ way  _ more stares with the scar in full view than when he’s wearing sunglasses when it’s dark out. Maybe people think it’s a fashion statement. Something like that. 

It’s not foolproof though, the guy who checks their tickets looks up at him and asks, “Bad sunburn?” 

To which Zuko nods, since explaining is never worth it. 

“What are we seeing?” Zuko asks Sokka as they enter the darkened theater, realizing he should have been more curious before. 

“A Beautiful Mind,” Sokka answers, “It’s not...yeah it’s a movie about a mathematician. And I love Nash equilibrium as a concept. But it’s more than that it’s about the guy’s struggle with who he is and the way he sees the world--I don’t know I thought you might find it interesting” 

“You brought me to see a movie about math, to get my mind off of math,” Zuko says drily. 

“Again, it’s not  _ really  _ that much about the math, it’s a human story. And--” 

“We’re human, so, that’s your logic, you’re a  _ genius  _ and that’s your logic!?” a smile creeps onto Zuko’s face, he’s barely stifling a laugh. 

“Shut up, I’m not talking to you for the rest of the movie.” Sokka fakes being greatly affronted and settles into his seat. 

Zuko looks at the number on his ticket stub, and sits to his right, dropping the sunglasses into the cupholder between them. “You’re not supposed to talk during movies anyway.” 

“You keep coming at me with the smart ass comebacks, I’m going to--assign you homework, that’s what I’m going to do,” Sokka whispers furiously. “You won’t even know what hit ya.” 

“I’m terrified,” Zuko says, and he’s smiling, glad that the theater is dark, and Sokka isn’t looking right at him. 

* * *

_ Differential, Session 13 _

The morning of the quiz Sokka texts ‘Good luck :)’. A half hour before the quiz he texts again, ‘Remember, stay calm’. Ten minutes before the quiz he texts yet one more time to say ‘I know you can do it’. If Zuko screenshots the text and saves it to a locked images folder on his phone, that’s his business. 

Five minutes before the quiz timer starts is when the spiral begins. Sokka’s sunken hours and hours of his time into preparing him for this. A thirty question test that’s supposed to assess calculus readiness. Not even any calculus itself. It’s overkill, it should be easy for Zuko to ace it. Sokka  _ must  _ be expecting him to ace it. Which is just what he needed, someone else to expect him to do well. To perform. So what if he can’t? 

Zuko tries to remember the movie. It’s been a couple days now, but he’d been calm during the movie. Happy even.  _ Fuck.  _ He should have studied more. But it’s too late now. 

By the time he opens the quiz site he’s lost focus entirely. The first questions are easy, he knows that they’re meant to be. But he circles C, then A, then B. Not because he thinks that’s correct but because he doesn’t want to lose time. He’s trying to read each question and start drawing out the important bits, actually drawing, like Sokka told him. The only thing that comes to mind though is his dad. 

He remembers the first time his dad yelled at his mom, and blamed her for the fact that he’s ‘slow’ with numbers. Dad never really raised his voice, much. But that made it worse, almost. Since that meant what he was saying wasn’t in the heat of the moment, or anything. He just really meant it. 

Maybe Zuko shouldn’t have laughed so much at Sokka’s occasional jokes. Maybe that’s the reason why the tutoring didn’t help. Why answering these questions still feels like trying to grab smoke out of thin air. He shouldn’t have started to enjoy it. Math is supposed to be hard. Numbers are disciplined. What he lacks is discipline, he’s been told that. 

He doesn’t even realize when the time stops. He’s answered barely half of the questions. After he hits submit he slams the computer shut. 

Sokka doesn’t stop texting. 

‘How did it go?’ 

‘Was there a lot of geometry, like I thought there’d be?’ 

‘Zuko?’ 

‘You there??’ 

Zuko just responds ‘I’m done’. 

* * *

_ Differential, Session 14 _

The next time Zuko’s supposed to go meet Sokka for a tutoring session, he simply doesn’t go. He just stays there in his room. Alone. 

After all of that. Being taught math with  _ love _ , because with Sokka math ‘is love’ (or so he says, all the time). It still didn’t work. Zuko can’t face him. Sokka’s always looked at him with bright eyes, he’s answered questions Zuko would find too stupid to ask anybody else. That would all change if Zuko tells him what grade he got on this quiz. It’s better to end on a high note. 

“Zuko, you are still here?” Uncle asks from the other side of the door. 

“Yes. I’m not going.” 

“Why not?” 

“I know you paid him a lot of money,” Zuko starts to explain, “I’ll try to find a way to pay you back.” 

“May I come in?” 

“Okay,” Zuko says. 

“Did he do something to upset you?” Uncle asks, stroking his chin. “He seemed like a nice boy.” 

_ He didn’t do anything, it was me. It’s always me.  _

“No.” 

Uncle sits at the foot of his bed. He looks at Zuko, then back at the floor. Then he waits. It’s one of his favorite strategies. He’ll wait for a minute or two, then start talking about something completely unrelated. Musicals that are in town. School board elections. Just wear Zuko out until he has to tell Uncle his problem, just to get him to leave. Sometimes Zuko wins the game, and listens to Uncle talk about things that he has no interest in, and still refuses to tell him anything. Usually not. Uncle is really stubborn. 

“I don’t think he’ll want to teach me anymore,” Zuko snaps. “Are you happy now?” 

“Did  _ he  _ say that?” Uncle asks. 

“Not in so many words, but--” 

“You have made the decision for him.” 

“I haven’t! I--It’s obvious okay. Some things are just obvious.” 

“Some things are,” Uncle nods, “But some may surprise you.” 

With that he gets up to leave. Zuko glares at his retreating back. So that’s it then? Uncle’s not gonna make him go?  _ That’s it?  _ Dad would have made him go. Dad wouldn’t have accepted him just not doing it. He would have expressed his displeasure more sharply. He would have made Zuko feel it. 

His phone buzzes. It’s Sokka. 

‘Running late?’ 

He gulps, then types out slowly, ‘Staying in today. I have allergies.’ 

* * *

_ Differential, Session 15 _

“I thought this was a tutoring day for you?” Katara asks. 

“It is,” Sokka says. 

She looks at the empty chair next to him. “Should I be concerned about you? More than usual?” 

“He just texted me he isn't coming. He has allergies.”

“Allergies.” Katara crosses her arms over her chest. 

“Yeah, allergies, you know, when your nose starts running and your head hurts and you’re all bleh.” 

“It’s an excuse, and it’s not a very good one,” she points out. 

“Can you stop being my sister for a second?” Sokka asks. 

“It’s not that easy, I’ve checked.” 

“I’m serious, could you pretend for a second you’re not my sister, and it’s not your mission in life to make fun of me. You’re just a friend. One of the guys.” 

“One of the guys?” Katara snorts, “You need Toph for this.” 

“Katara!” 

“Okay, okay, fine.” 

“I think he’s tired of me, or weirded out. I took him to this kinda nerdy movie. And I talk about how much I love math. All the time. I texted him good luck, a couple times before he had this quiz. Then he started acting differently. He said he’s done, and I don’t know what that meant. Done with me, or...” 

Katara’s expression softens a bit and she sits in the empty chair. Zuko’s chair. “Sokka, maybe it’s the quiz. Not you.” 

“What?” 

“As annoying as you are, I don’t think he quit tutoring because of you.” 

Sokka’s head starts spinning. The quiz. The quiz. The quiz. Maybe…?  _ No. No way.  _

Sokka puts two and two together. Kisses his sister on the forehead, then sprints out of the house. “Thank you! Love you! Bye!” 

* * *

_ Differential, Session 16 _

There’s another knock on Zuko’s door. 

“Uncle, I said I’m not going!” he snaps, then lays his head back down on his pillow. It’s a stay in bed and wallow in misery type of day. 

“It’s me, actually.” 

_ Sokka????? _

“I know you said you had allergies so you couldn’t come outside, so I thought I’d come to you. I come in peace.” Sokka knocks again. “If you really don’t want to see me, I can go. I just thought--” 

Zuko’s heart rate picks up as he walks towards the door. He didn’t want to do this in person. 

“Your hair,” Sokka starts saying as he opens the door. 

“My--” Zuko reaches up and pats it down, of course it would be sticking up all over the place at a moment like this.  _ Of course.  _

“Can I close the door?” Sokka asks. 

“Yeah. Fine.” 

“Um,” Sokka clears his throat. 

“I guess you wanna talk about the quiz I took.” Zuko can’t meet his eyes. 

“No,” Sokka says, “Did I ever tell you about my first math contest?” 

“No.” 

Zuko sits back down on the bed, and Sokka sits himself on Zuko’s computer chair. The black one that spins. 

“It was freshman year of high school,” Sokka starts, “I was the number one qualifier from the school. They sent me, and these two other guys. I got to the auditorium where they held it, and there were all these chairs. Rows and rows of chairs, okay?” 

“Okay.” 

“This girl came up to me, and asked me for my name, since all the chairs were labelled. I’m guessing alphabetically. Do you know what I said?” 

“Your name?” 

“I had been cramming the night before. Out of this multiple choice test book that was compiled by a bunch of professors. And I was still going through a problem in my head when she came up to me, and I was kind of a mess, so I said ‘none of the above’.” 

_ Oh my god.  _

“I did eventually end up finding my seat,” Sokka explains, “But I was pretty embarrassed by then. And I thought things couldn’t possibly get any worse. They passed out the booklets, and I started taking the test. Then I threw up.” 

“That’s disgusting.” 

“I know.” 

“If this is supposed to make me feel better--” Zuko sputters, “It’s not going to work. I bombed it, and not just because I had an upset stomach that day. I just didn’t get it.” 

“Okay?!” Zuko snaps again, “I didn’t get it. It didn’t work!” 

“It’s okay, doesn’t matter,” Sokka says. His voice is soft and his eyes are kind. Zuko thinks he might break. 

“When I came home the night of the competition and I told my dad what happened, and that I knew that no one in our family had been to college and if I kept this up no one ever would, he told me it didn’t matter. How I did didn’t matter. It just mattered that I got up there and I did it.” 

Sokka takes off the backpack he’s carrying and fishes around for some papers. Zuko uses the time to calm himself down. 

Sokka puts some worksheets on the desk, then takes Zuko’s hands in his. Just barely. His touch is warm and his hands are soft and Zuko wonders if he might be hallucinating. 

“All I ever want you to do is show up, and I’m going to be with you every step of the way.”

“You can’t--” 

“Uh-uh. Lips moving, still talking. Don’t try me, I grew up with Katara, I know how to get my point in. I already know you can do this. We’re just going to show everyone else.” 

“But--” 

Sokka lets go of his hands, and he smiles. His eyes are so blue, and Zuko wonders if he could just look at them and see the way they see patterns and letters and numbers. The way Sokka sees him. “Zuko, I promise.” 

**Notes for the Chapter:**

> ty all for lovely comments and for liking this fic <3333  
> at this point im using the 'session #' headings just to connotate pov shifts between zuko and sokka (sort of like i did in operation leverage)  
> also the plotpoint of sokka undermining ozai's thesis wasn't in the original draft, but i rlly think its worth it, fuck ozai
> 
> also the story is still gonna have three parts  
> \--differential  
> \--integral  
> \--fundamental theorem of calculus which binds the two together
> 
> to correspond to stages in their relationship

**Author's Note:**

> I’m nowhere near as smart as sokka in this fic but I was a calc tutor  
> The hardest part of modern setting ATLA fics is giving everyone who isn’t Toph a dang lastname


End file.
